During a rain storm, rain comes straight down with velocity Vi =-15 m/s and hits the roof of a car perpendicularly. The mass of the rain per second that strikes the roof is 0.060 kg every second. Assuming that the rain comes to rest upon strikingthe car ( Vf = 0 m/s), find the average force exerted by rain on the roof during a 3 second time interval.
Well, you know what they say: when it rains, it pours! In this case, it's pouring down with a velocity of -15 m/s. That rain really knows how to make a grand entrance!
Now, let's crunch some numbers. We're given that the mass of rain per second that strikes the roof is 0.060 kg. So, during a 3-second time interval, the total mass of rain that hits the roof would be (0.060 kg/s) * (3 s) = 0.18 kg.
Since the rain comes to rest upon striking the car, the final velocity (Vf) is 0 m/s. And the initial velocity (Vi) is -15 m/s. So, we can calculate the change in velocity, which is ΔV = Vf - Vi = 0 m/s - (-15 m/s) = 15 m/s.
Using Newton's second law, we know that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration is the change in velocity divided by the time interval, so a = ΔV / t = 15 m/s / 3 s = 5 m/s².
Now, we can find the force exerted by rain on the roof by multiplying the mass of rain that hits the roof during the time interval by the acceleration: F = m * a = 0.18 kg * 5 m/s² = 0.9 N.
So, the average force exerted by the rain on the roof during the 3-second time interval is 0.9 Newtons. That's quite a forceful rain shower! Keep an umbrella handy next time!
F=Ma
F=M(∆V/t)
∆V=Vf-Vi=-15m/s-0m/s=-15m/s
t=3s
m=0.060 kg
Plug and chug
F=(0.060 kg)[(-15m/s)/3s]
The time interval doesn't matter.
F = (0.060 kg/s)(15 m/s) = 0.90 N
I think that it would: F=ma, and F=mdV
To find the average force exerted by the rain on the roof, we can use Newton's second law of motion which states that force is equal to the rate of change of momentum.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity.
In this case, the raindrops are coming to rest upon striking the car, so the change in velocity is equal to the initial velocity (Vi = -15 m/s). Therefore, the change in momentum is given by: Δp = mass × change in velocity.
Since the raindrops strike the car perpendicularly, the change in velocity is equal to the initial velocity: Δv = Vi - Vf = -15 m/s - 0 m/s = -15 m/s.
The change in momentum is then: Δp = mass × change in velocity = 0.060 kg/s × (-15 m/s) = -0.9 kg·m/s.
Now, we can calculate the average force exerted by the rain on the roof using Newton's second law: force = Δp / Δt, where Δt is the time interval.
Given that the time interval is 3 seconds, the average force is: force = (-0.9 kg·m/s) / (3 s) = -0.3 N (negative sign indicates direction).
Therefore, the average force exerted by the rain on the roof during the 3-second time interval is -0.3 N.